The atmospheric oxidation of dimethyl sulfide and other emitted sulfur species leads to the formation of the methylthio radical, CH₃S, which can be further oxidized to the CH₃SO and CH₃SO₂ radicals. We investigated computationally the reactions of these three sulfur-centered radicals with the peroxy radicals ROO and HOO. Our results demonstrate that CH₃S and CH₃SO react with these peroxy radicals to form short-lived peroxide intermediates, which then decompose via a concerted O-O bond scission and S═O double bond formation that results in an increased valence of the sulfur atom. In contrast, CH₃SO₂ reacts to form stable CH₃S(O)₂OOR and CH₃S(O)₂OOH peroxide products, as sulfur is already at its highest valence. Multireference methods were used to describe these reactions in which the valence of the sulfur atom changes.